There is a bag filled with 2 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?

Question:

A bag with 2 blue (B), 4 red (R) and 5 green (G) marbles (total 11 marbles).

Two are drawn at random without replacement.

Find probability of getting two marbles of same colour.

Solution:

We can get either 2B, 2R or 2G as successful outcomes.

To get two blue marbles (2B),

probability of the first one being blue = P(B)=2/11

probability of the second blue marble = P(-B)=1/10 (one left out of 10 left)

Probability that both are blue (use multiplication rule)

P(2B)=(2/11)(1/10)=2/110

Similarly, for two red marbles

P(2R)=(4/11)(3/10)=12/110

and for two green marbles

P(2G)=(5/11)(4/10)=20/110

Since all three events 2B, 2R and 2G are mutually exclusive, the probability

that any one can happen is the sum of the individual probabilities, thus

probability of getting two marbles of the same colour (without replacement)

=P(2B)+P(2R)+P(2G)

=2/110 + 12/110 + 20/110

=34/110

= 17/55

Step-by-step explanation:

4/11

hope this helps

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step-by-step explanation:

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